Polytope of Type {32,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {32,12}*768a
Also Known As : {32,12|2}. if this polytope has another name.
Group : SmallGroup(768,90208)
Rank : 3
Schlafli Type : {32,12}
Number of vertices, edges, etc : 32, 192, 12
Order of s0s1s2 : 96
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {16,12}*384a, {32,6}*384
3-fold quotients : {32,4}*256a
4-fold quotients : {8,12}*192a, {16,6}*192
6-fold quotients : {16,4}*128a, {32,2}*128
8-fold quotients : {4,12}*96a, {8,6}*96
12-fold quotients : {8,4}*64a, {16,2}*64
16-fold quotients : {2,12}*48, {4,6}*48a
24-fold quotients : {4,4}*32, {8,2}*32
32-fold quotients : {2,6}*24
48-fold quotients : {2,4}*16, {4,2}*16
64-fold quotients : {2,3}*12
96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,193)( 2,194)( 3,195)( 4,196)( 5,197)( 6,198)( 7,202)( 8,203)
( 9,204)( 10,199)( 11,200)( 12,201)( 13,211)( 14,212)( 15,213)( 16,214)
( 17,215)( 18,216)( 19,205)( 20,206)( 21,207)( 22,208)( 23,209)( 24,210)
( 25,217)( 26,218)( 27,219)( 28,220)( 29,221)( 30,222)( 31,226)( 32,227)
( 33,228)( 34,223)( 35,224)( 36,225)( 37,235)( 38,236)( 39,237)( 40,238)
( 41,239)( 42,240)( 43,229)( 44,230)( 45,231)( 46,232)( 47,233)( 48,234)
( 49,253)( 50,254)( 51,255)( 52,256)( 53,257)( 54,258)( 55,262)( 56,263)
( 57,264)( 58,259)( 59,260)( 60,261)( 61,241)( 62,242)( 63,243)( 64,244)
( 65,245)( 66,246)( 67,250)( 68,251)( 69,252)( 70,247)( 71,248)( 72,249)
( 73,277)( 74,278)( 75,279)( 76,280)( 77,281)( 78,282)( 79,286)( 80,287)
( 81,288)( 82,283)( 83,284)( 84,285)( 85,265)( 86,266)( 87,267)( 88,268)
( 89,269)( 90,270)( 91,274)( 92,275)( 93,276)( 94,271)( 95,272)( 96,273)
( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,298)(104,299)
(105,300)(106,295)(107,296)(108,297)(109,307)(110,308)(111,309)(112,310)
(113,311)(114,312)(115,301)(116,302)(117,303)(118,304)(119,305)(120,306)
(121,313)(122,314)(123,315)(124,316)(125,317)(126,318)(127,322)(128,323)
(129,324)(130,319)(131,320)(132,321)(133,331)(134,332)(135,333)(136,334)
(137,335)(138,336)(139,325)(140,326)(141,327)(142,328)(143,329)(144,330)
(145,349)(146,350)(147,351)(148,352)(149,353)(150,354)(151,358)(152,359)
(153,360)(154,355)(155,356)(156,357)(157,337)(158,338)(159,339)(160,340)
(161,341)(162,342)(163,346)(164,347)(165,348)(166,343)(167,344)(168,345)
(169,373)(170,374)(171,375)(172,376)(173,377)(174,378)(175,382)(176,383)
(177,384)(178,379)(179,380)(180,381)(181,361)(182,362)(183,363)(184,364)
(185,365)(186,366)(187,370)(188,371)(189,372)(190,367)(191,368)(192,369);;
s1 := ( 2, 3)( 5, 6)( 7, 10)( 8, 12)( 9, 11)( 13, 19)( 14, 21)( 15, 20)
( 16, 22)( 17, 24)( 18, 23)( 26, 27)( 29, 30)( 31, 34)( 32, 36)( 33, 35)
( 37, 43)( 38, 45)( 39, 44)( 40, 46)( 41, 48)( 42, 47)( 49, 61)( 50, 63)
( 51, 62)( 52, 64)( 53, 66)( 54, 65)( 55, 70)( 56, 72)( 57, 71)( 58, 67)
( 59, 69)( 60, 68)( 73, 85)( 74, 87)( 75, 86)( 76, 88)( 77, 90)( 78, 89)
( 79, 94)( 80, 96)( 81, 95)( 82, 91)( 83, 93)( 84, 92)( 97,121)( 98,123)
( 99,122)(100,124)(101,126)(102,125)(103,130)(104,132)(105,131)(106,127)
(107,129)(108,128)(109,139)(110,141)(111,140)(112,142)(113,144)(114,143)
(115,133)(116,135)(117,134)(118,136)(119,138)(120,137)(145,181)(146,183)
(147,182)(148,184)(149,186)(150,185)(151,190)(152,192)(153,191)(154,187)
(155,189)(156,188)(157,169)(158,171)(159,170)(160,172)(161,174)(162,173)
(163,178)(164,180)(165,179)(166,175)(167,177)(168,176)(193,241)(194,243)
(195,242)(196,244)(197,246)(198,245)(199,250)(200,252)(201,251)(202,247)
(203,249)(204,248)(205,259)(206,261)(207,260)(208,262)(209,264)(210,263)
(211,253)(212,255)(213,254)(214,256)(215,258)(216,257)(217,265)(218,267)
(219,266)(220,268)(221,270)(222,269)(223,274)(224,276)(225,275)(226,271)
(227,273)(228,272)(229,283)(230,285)(231,284)(232,286)(233,288)(234,287)
(235,277)(236,279)(237,278)(238,280)(239,282)(240,281)(289,361)(290,363)
(291,362)(292,364)(293,366)(294,365)(295,370)(296,372)(297,371)(298,367)
(299,369)(300,368)(301,379)(302,381)(303,380)(304,382)(305,384)(306,383)
(307,373)(308,375)(309,374)(310,376)(311,378)(312,377)(313,337)(314,339)
(315,338)(316,340)(317,342)(318,341)(319,346)(320,348)(321,347)(322,343)
(323,345)(324,344)(325,355)(326,357)(327,356)(328,358)(329,360)(330,359)
(331,349)(332,351)(333,350)(334,352)(335,354)(336,353);;
s2 := ( 1, 99)( 2, 98)( 3, 97)( 4,102)( 5,101)( 6,100)( 7,105)( 8,104)
( 9,103)( 10,108)( 11,107)( 12,106)( 13,111)( 14,110)( 15,109)( 16,114)
( 17,113)( 18,112)( 19,117)( 20,116)( 21,115)( 22,120)( 23,119)( 24,118)
( 25,123)( 26,122)( 27,121)( 28,126)( 29,125)( 30,124)( 31,129)( 32,128)
( 33,127)( 34,132)( 35,131)( 36,130)( 37,135)( 38,134)( 39,133)( 40,138)
( 41,137)( 42,136)( 43,141)( 44,140)( 45,139)( 46,144)( 47,143)( 48,142)
( 49,147)( 50,146)( 51,145)( 52,150)( 53,149)( 54,148)( 55,153)( 56,152)
( 57,151)( 58,156)( 59,155)( 60,154)( 61,159)( 62,158)( 63,157)( 64,162)
( 65,161)( 66,160)( 67,165)( 68,164)( 69,163)( 70,168)( 71,167)( 72,166)
( 73,171)( 74,170)( 75,169)( 76,174)( 77,173)( 78,172)( 79,177)( 80,176)
( 81,175)( 82,180)( 83,179)( 84,178)( 85,183)( 86,182)( 87,181)( 88,186)
( 89,185)( 90,184)( 91,189)( 92,188)( 93,187)( 94,192)( 95,191)( 96,190)
(193,291)(194,290)(195,289)(196,294)(197,293)(198,292)(199,297)(200,296)
(201,295)(202,300)(203,299)(204,298)(205,303)(206,302)(207,301)(208,306)
(209,305)(210,304)(211,309)(212,308)(213,307)(214,312)(215,311)(216,310)
(217,315)(218,314)(219,313)(220,318)(221,317)(222,316)(223,321)(224,320)
(225,319)(226,324)(227,323)(228,322)(229,327)(230,326)(231,325)(232,330)
(233,329)(234,328)(235,333)(236,332)(237,331)(238,336)(239,335)(240,334)
(241,339)(242,338)(243,337)(244,342)(245,341)(246,340)(247,345)(248,344)
(249,343)(250,348)(251,347)(252,346)(253,351)(254,350)(255,349)(256,354)
(257,353)(258,352)(259,357)(260,356)(261,355)(262,360)(263,359)(264,358)
(265,363)(266,362)(267,361)(268,366)(269,365)(270,364)(271,369)(272,368)
(273,367)(274,372)(275,371)(276,370)(277,375)(278,374)(279,373)(280,378)
(281,377)(282,376)(283,381)(284,380)(285,379)(286,384)(287,383)(288,382);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(384)!( 1,193)( 2,194)( 3,195)( 4,196)( 5,197)( 6,198)( 7,202)
( 8,203)( 9,204)( 10,199)( 11,200)( 12,201)( 13,211)( 14,212)( 15,213)
( 16,214)( 17,215)( 18,216)( 19,205)( 20,206)( 21,207)( 22,208)( 23,209)
( 24,210)( 25,217)( 26,218)( 27,219)( 28,220)( 29,221)( 30,222)( 31,226)
( 32,227)( 33,228)( 34,223)( 35,224)( 36,225)( 37,235)( 38,236)( 39,237)
( 40,238)( 41,239)( 42,240)( 43,229)( 44,230)( 45,231)( 46,232)( 47,233)
( 48,234)( 49,253)( 50,254)( 51,255)( 52,256)( 53,257)( 54,258)( 55,262)
( 56,263)( 57,264)( 58,259)( 59,260)( 60,261)( 61,241)( 62,242)( 63,243)
( 64,244)( 65,245)( 66,246)( 67,250)( 68,251)( 69,252)( 70,247)( 71,248)
( 72,249)( 73,277)( 74,278)( 75,279)( 76,280)( 77,281)( 78,282)( 79,286)
( 80,287)( 81,288)( 82,283)( 83,284)( 84,285)( 85,265)( 86,266)( 87,267)
( 88,268)( 89,269)( 90,270)( 91,274)( 92,275)( 93,276)( 94,271)( 95,272)
( 96,273)( 97,289)( 98,290)( 99,291)(100,292)(101,293)(102,294)(103,298)
(104,299)(105,300)(106,295)(107,296)(108,297)(109,307)(110,308)(111,309)
(112,310)(113,311)(114,312)(115,301)(116,302)(117,303)(118,304)(119,305)
(120,306)(121,313)(122,314)(123,315)(124,316)(125,317)(126,318)(127,322)
(128,323)(129,324)(130,319)(131,320)(132,321)(133,331)(134,332)(135,333)
(136,334)(137,335)(138,336)(139,325)(140,326)(141,327)(142,328)(143,329)
(144,330)(145,349)(146,350)(147,351)(148,352)(149,353)(150,354)(151,358)
(152,359)(153,360)(154,355)(155,356)(156,357)(157,337)(158,338)(159,339)
(160,340)(161,341)(162,342)(163,346)(164,347)(165,348)(166,343)(167,344)
(168,345)(169,373)(170,374)(171,375)(172,376)(173,377)(174,378)(175,382)
(176,383)(177,384)(178,379)(179,380)(180,381)(181,361)(182,362)(183,363)
(184,364)(185,365)(186,366)(187,370)(188,371)(189,372)(190,367)(191,368)
(192,369);
s1 := Sym(384)!( 2, 3)( 5, 6)( 7, 10)( 8, 12)( 9, 11)( 13, 19)( 14, 21)
( 15, 20)( 16, 22)( 17, 24)( 18, 23)( 26, 27)( 29, 30)( 31, 34)( 32, 36)
( 33, 35)( 37, 43)( 38, 45)( 39, 44)( 40, 46)( 41, 48)( 42, 47)( 49, 61)
( 50, 63)( 51, 62)( 52, 64)( 53, 66)( 54, 65)( 55, 70)( 56, 72)( 57, 71)
( 58, 67)( 59, 69)( 60, 68)( 73, 85)( 74, 87)( 75, 86)( 76, 88)( 77, 90)
( 78, 89)( 79, 94)( 80, 96)( 81, 95)( 82, 91)( 83, 93)( 84, 92)( 97,121)
( 98,123)( 99,122)(100,124)(101,126)(102,125)(103,130)(104,132)(105,131)
(106,127)(107,129)(108,128)(109,139)(110,141)(111,140)(112,142)(113,144)
(114,143)(115,133)(116,135)(117,134)(118,136)(119,138)(120,137)(145,181)
(146,183)(147,182)(148,184)(149,186)(150,185)(151,190)(152,192)(153,191)
(154,187)(155,189)(156,188)(157,169)(158,171)(159,170)(160,172)(161,174)
(162,173)(163,178)(164,180)(165,179)(166,175)(167,177)(168,176)(193,241)
(194,243)(195,242)(196,244)(197,246)(198,245)(199,250)(200,252)(201,251)
(202,247)(203,249)(204,248)(205,259)(206,261)(207,260)(208,262)(209,264)
(210,263)(211,253)(212,255)(213,254)(214,256)(215,258)(216,257)(217,265)
(218,267)(219,266)(220,268)(221,270)(222,269)(223,274)(224,276)(225,275)
(226,271)(227,273)(228,272)(229,283)(230,285)(231,284)(232,286)(233,288)
(234,287)(235,277)(236,279)(237,278)(238,280)(239,282)(240,281)(289,361)
(290,363)(291,362)(292,364)(293,366)(294,365)(295,370)(296,372)(297,371)
(298,367)(299,369)(300,368)(301,379)(302,381)(303,380)(304,382)(305,384)
(306,383)(307,373)(308,375)(309,374)(310,376)(311,378)(312,377)(313,337)
(314,339)(315,338)(316,340)(317,342)(318,341)(319,346)(320,348)(321,347)
(322,343)(323,345)(324,344)(325,355)(326,357)(327,356)(328,358)(329,360)
(330,359)(331,349)(332,351)(333,350)(334,352)(335,354)(336,353);
s2 := Sym(384)!( 1, 99)( 2, 98)( 3, 97)( 4,102)( 5,101)( 6,100)( 7,105)
( 8,104)( 9,103)( 10,108)( 11,107)( 12,106)( 13,111)( 14,110)( 15,109)
( 16,114)( 17,113)( 18,112)( 19,117)( 20,116)( 21,115)( 22,120)( 23,119)
( 24,118)( 25,123)( 26,122)( 27,121)( 28,126)( 29,125)( 30,124)( 31,129)
( 32,128)( 33,127)( 34,132)( 35,131)( 36,130)( 37,135)( 38,134)( 39,133)
( 40,138)( 41,137)( 42,136)( 43,141)( 44,140)( 45,139)( 46,144)( 47,143)
( 48,142)( 49,147)( 50,146)( 51,145)( 52,150)( 53,149)( 54,148)( 55,153)
( 56,152)( 57,151)( 58,156)( 59,155)( 60,154)( 61,159)( 62,158)( 63,157)
( 64,162)( 65,161)( 66,160)( 67,165)( 68,164)( 69,163)( 70,168)( 71,167)
( 72,166)( 73,171)( 74,170)( 75,169)( 76,174)( 77,173)( 78,172)( 79,177)
( 80,176)( 81,175)( 82,180)( 83,179)( 84,178)( 85,183)( 86,182)( 87,181)
( 88,186)( 89,185)( 90,184)( 91,189)( 92,188)( 93,187)( 94,192)( 95,191)
( 96,190)(193,291)(194,290)(195,289)(196,294)(197,293)(198,292)(199,297)
(200,296)(201,295)(202,300)(203,299)(204,298)(205,303)(206,302)(207,301)
(208,306)(209,305)(210,304)(211,309)(212,308)(213,307)(214,312)(215,311)
(216,310)(217,315)(218,314)(219,313)(220,318)(221,317)(222,316)(223,321)
(224,320)(225,319)(226,324)(227,323)(228,322)(229,327)(230,326)(231,325)
(232,330)(233,329)(234,328)(235,333)(236,332)(237,331)(238,336)(239,335)
(240,334)(241,339)(242,338)(243,337)(244,342)(245,341)(246,340)(247,345)
(248,344)(249,343)(250,348)(251,347)(252,346)(253,351)(254,350)(255,349)
(256,354)(257,353)(258,352)(259,357)(260,356)(261,355)(262,360)(263,359)
(264,358)(265,363)(266,362)(267,361)(268,366)(269,365)(270,364)(271,369)
(272,368)(273,367)(274,372)(275,371)(276,370)(277,375)(278,374)(279,373)
(280,378)(281,377)(282,376)(283,381)(284,380)(285,379)(286,384)(287,383)
(288,382);
poly := sub<Sym(384)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope